where \(m(i)\)  is the methylation level of the \(i\) -th dimer. Due to cooperativity, all dimers in one cluster change their activity state simultaneously and this transition probability depends on the free energy of the cluster (see Appendix  for more details). The activity of a cluster is defined as the probability to find the cluster in the active state and its long time average is given by \([1+\exp (F)]^{-1}\) . The total activity of the cell is obtained by averaging over activities of all clusters. When clusters are larger in size, they are fewer in number and the total activity is then a result of averaging over a smaller number of clusters. This is why activity fluctuations increase for large \(n\)  [1]}, [2]}.
